Problem: If the line y=mx+1 intersects the ellipse x2+4y2=1 exactly once, then the value of m2 is
Answer Choices:
A. 21
B. 32
C. 43
D. 34
E. 65
Solution:
Exactly one intersection requires the roots of the quadratic x2+4(mx+1)2=1 to be equal and hence the discriminant to be zero. i.e. (8m)2−4(4m2+1)⋅3= 0 . Hence m2=43.